Question

topic: integral calculus, help me to integrate this pleasee, Integral of (2 + 5/x)^2 dx

Answer 1

\[\int\limits (2 + 5/x)^2 dx\]

Answer 2

@iGreen @MARC_ @nikvist

Answer 3

@phi

Answer 4

@ilo

Answer 5

@Ilovecake

Answer 6

simplest is just expand the brackets and do each term

Answer 7

so it will become (4+ 25/x^2 ?

Answer 8

@Ilovecake

Answer 9

Yes

Answer 10

then

Answer 11

no no no

Answer 12

how? @IrishBoy123

Answer 13

(2+ 5/x) times (2+ 5/x)

Answer 14

ah , what should i do next

Answer 15

do that expansion then integrate each bit separately.

Answer 16

i will multiply it each by piece?

Answer 17

@IrishBoy123

Answer 18

yep post yr answer here

Answer 19

( 4 + 10/x+10/x +4)

Answer 20

@IrishBoy123

Answer 21

is the original expression
\[ \left(2 + \frac{5}{x}\right)^2 \]

Answer 22

yes

Answer 23

after squaring did you get
\[ 4 + \frac{25}{x^2} + \frac{20}{x} \]

Answer 24

yes then what will i do

Answer 25

write the problem as
\[ 4\int \ dx + 25\int x^{-2} \ dx + 20 \int \frac{dx}{x} \]

Answer 26

I assume you can do some of those integrals ?

Answer 27

i dont know what to do next

Answer 28

are you saying you don't know how to do
\[ 4 \int dx \]
?

Answer 29

yes

Answer 30

the integral of dx is x

based on this question, they expect you to know quite a bit of integral calculus, and
integral of dx is the first baby step, which means you have to learn a lot of stuff to do this problem. And it's very hard to learn or teach calculus typing into this box.

Maybe watch Khan's videos
https://www.khanacademy.org/math/integral-calculus/indefinite-definite-integrals/indefinite_integrals/v/antiderivatives-and-indefinite-integrals